Description of the Data The dataset contains detailed information on reported crimes, categorized by type, location, and time. It includes columns such as:
Date: The date of the occurrence. Time: The time of the occurrence. Latitude and Longitude: Geographical coordinates of the incident. Offense Category: The type of crime, such as larceny, vandalism, or burglary. Violent/Property Crime Indicator: Classification of crimes as violent or property-related. Domestic: Indicates if the crime was domestic in nature. Total Incidents: Number of incidents reported for a specific category. The data spans multiple years and includes seasonality, trend, and random components. By analyzing these elements, we aim to uncover patterns and develop reliable forecasting models to predict future crime occurrences.
Objective: Using advanced time-series methods such as ARIMA, STL decomposition, and Holt-Winters, the analysis aims to identify the most accurate model for predicting crime trends in various categories, thus enabling actionable insights.Importance: Accurately forecasting crime trends is vital for law enforcement, policymakers, and communities. By understanding the future trajectory of specific crime categories, stakeholders can proactively address challenges, optimize resource allocation, and implement preventive measures. This analysis supports data-driven decision-making, enhancing public safety and fostering community well-being.
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## accuracy
We would cut the data at 2001
New
column names to be applied Date Time Lat Lon Cat VP Domestic Tot_Inc
19118 1999-12-31 19:30:00 NA NA Larceny Part I N 1 37292 1999-12-31
20:30:00 NA NA Larceny Part I N 1 119123 1999-12-31 20:00:00 NA NA
Vandalism Part II N 1 9379 2000-01-01 12:01:00 NA NA Larceny Part I N 1
10733 2000-01-01 11:00:00 NA NA Larceny Part I N 1 20324 2000-01-01
12:01:00 NA NA Forgery Part II N 1
density
plot for crime rate based on lattitude and longitude
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There appears to be seasonality in the time series, indicating the
increase of crime in specific
days.
The
residuals are randomly distributed, shows no pattern. This means that
the Naive forecast is being able to capture the seasonality and trend
Since
the histogram is normal, it means that the Naive Forecast might be a
good method in this case.
Forecast
assumes future values equal the mean of past values.
Observing
the residuals, we can say the Mean Forecast doesnot effectively captures
the pattern. Since the existence of patterns in residuals, it suggest
the models limitations.
Since the residuals do not show patterns, this suggests that the model
is capturing the seasonality or trend.
Similar
to the one without drift , residuals are randomly distributed; absence
of patterns suggest no accounted trends or seasonality.
SES
can be effective because it uses a weighted average of past values,
putting more weight on recent observations without explicitly modeling
trend or seasonality.
Since there is a significant overlap between the original timeseries and
seasonally independent timeseries, seasonality is not very pronounced.
Factors like trend or randomness moght have bigger influence on the
data.
[1]
“Number of differences required for stationarity: 1”
Fitting models using approximations to speed things up…
ARIMA(0,1,0) : 3247.037 ARIMA(0,1,0) with drift : 3249.007 ARIMA(0,1,0)(0,0,1)[12] : 3237.545 ARIMA(0,1,0)(0,0,1)[12] with drift : 3239.523 ARIMA(0,1,0)(0,0,2)[12] : 3237.29 ARIMA(0,1,0)(0,0,2)[12] with drift : 3239.277 ARIMA(0,1,0)(1,0,0)[12] : 3204.453 ARIMA(0,1,0)(1,0,0)[12] with drift : 3206.394 ARIMA(0,1,0)(1,0,1)[12] : 3204.482 ARIMA(0,1,0)(1,0,1)[12] with drift : 3206.477 ARIMA(0,1,0)(1,0,2)[12] : 3203.137 ARIMA(0,1,0)(1,0,2)[12] with drift : 3205.167 ARIMA(0,1,0)(2,0,0)[12] : 3204.508 ARIMA(0,1,0)(2,0,0)[12] with drift : 3206.511 ARIMA(0,1,0)(2,0,1)[12] : Inf ARIMA(0,1,0)(2,0,1)[12] with drift : Inf ARIMA(0,1,0)(2,0,2)[12] : Inf ARIMA(0,1,0)(2,0,2)[12] with drift : Inf ARIMA(0,1,1) : 3199.389 ARIMA(0,1,1) with drift : 3201.038 ARIMA(0,1,1)(0,0,1)[12] : 3190.258 ARIMA(0,1,1)(0,0,1)[12] with drift : 3191.986 ARIMA(0,1,1)(0,0,2)[12] : 3188.588 ARIMA(0,1,1)(0,0,2)[12] with drift : 3190.33 ARIMA(0,1,1)(1,0,0)[12] : 3125.141 ARIMA(0,1,1)(1,0,0)[12] with drift : 3127.194 ARIMA(0,1,1)(1,0,1)[12] : 3121.32 ARIMA(0,1,1)(1,0,1)[12] with drift : 3123.372 ARIMA(0,1,1)(1,0,2)[12] : 3111.57 ARIMA(0,1,1)(1,0,2)[12] with drift : 3113.577 ARIMA(0,1,1)(2,0,0)[12] : 3117.113 ARIMA(0,1,1)(2,0,0)[12] with drift : 3119.146 ARIMA(0,1,1)(2,0,1)[12] : Inf ARIMA(0,1,1)(2,0,1)[12] with drift : Inf ARIMA(0,1,1)(2,0,2)[12] : Inf ARIMA(0,1,1)(2,0,2)[12] with drift : Inf ARIMA(0,1,2) : 3201.152 ARIMA(0,1,2) with drift : 3202.786 ARIMA(0,1,2)(0,0,1)[12] : 3192.225 ARIMA(0,1,2)(0,0,1)[12] with drift : 3193.958 ARIMA(0,1,2)(0,0,2)[12] : 3190.614 ARIMA(0,1,2)(0,0,2)[12] with drift : 3192.364 ARIMA(0,1,2)(1,0,0)[12] : 3125.941 ARIMA(0,1,2)(1,0,0)[12] with drift : 3128.009 ARIMA(0,1,2)(1,0,1)[12] : 3121.431 ARIMA(0,1,2)(1,0,1)[12] with drift : 3123.428 ARIMA(0,1,2)(1,0,2)[12] : 3112.274 ARIMA(0,1,2)(1,0,2)[12] with drift : 3114.222 ARIMA(0,1,2)(2,0,0)[12] : 3118.248 ARIMA(0,1,2)(2,0,0)[12] with drift : 3120.265 ARIMA(0,1,2)(2,0,1)[12] : Inf ARIMA(0,1,2)(2,0,1)[12] with drift : Inf ARIMA(0,1,3) : 3202.036 ARIMA(0,1,3) with drift : 3203.624 ARIMA(0,1,3)(0,0,1)[12] : 3194.019 ARIMA(0,1,3)(0,0,1)[12] with drift : 3195.746 ARIMA(0,1,3)(0,0,2)[12] : 3192.594 ARIMA(0,1,3)(0,0,2)[12] with drift : 3194.349 ARIMA(0,1,3)(1,0,0)[12] : 3123.409 ARIMA(0,1,3)(1,0,0)[12] with drift : 3125.471 ARIMA(0,1,3)(1,0,1)[12] : 3116.114 ARIMA(0,1,3)(1,0,1)[12] with drift : 3117.889 ARIMA(0,1,3)(2,0,0)[12] : 3115.711 ARIMA(0,1,3)(2,0,0)[12] with drift : 3117.591 ARIMA(0,1,4) : 3203.986 ARIMA(0,1,4) with drift : 3205.568 ARIMA(0,1,4)(0,0,1)[12] : 3196.102 ARIMA(0,1,4)(0,0,1)[12] with drift : 3197.843 ARIMA(0,1,4)(1,0,0)[12] : 3123.281 ARIMA(0,1,4)(1,0,0)[12] with drift : 3125.352 ARIMA(0,1,5) : 3205.652 ARIMA(0,1,5) with drift : 3207.278 ARIMA(1,1,0) : 3170.336 ARIMA(1,1,0) with drift : 3172.345 ARIMA(1,1,0)(0,0,1)[12] : 3154.501 ARIMA(1,1,0)(0,0,1)[12] with drift : 3156.529 ARIMA(1,1,0)(0,0,2)[12] : 3153.158 ARIMA(1,1,0)(0,0,2)[12] with drift : 3155.195 ARIMA(1,1,0)(1,0,0)[12] : 3142.964 ARIMA(1,1,0)(1,0,0)[12] with drift : 3144.987 ARIMA(1,1,0)(1,0,1)[12] : 3144.872 ARIMA(1,1,0)(1,0,1)[12] with drift : 3146.915 ARIMA(1,1,0)(1,0,2)[12] : 3142.916 ARIMA(1,1,0)(1,0,2)[12] with drift : 3144.992 ARIMA(1,1,0)(2,0,0)[12] : 3145.232 ARIMA(1,1,0)(2,0,0)[12] with drift : 3147.294 ARIMA(1,1,0)(2,0,1)[12] : Inf ARIMA(1,1,0)(2,0,1)[12] with drift : Inf ARIMA(1,1,0)(2,0,2)[12] : Inf ARIMA(1,1,0)(2,0,2)[12] with drift : Inf ARIMA(1,1,1) : 3128.264 ARIMA(1,1,1) with drift : 3130.011 ARIMA(1,1,1)(0,0,1)[12] : 3116.125 ARIMA(1,1,1)(0,0,1)[12] with drift : 3117.998 ARIMA(1,1,1)(0,0,2)[12] : 3109.291 ARIMA(1,1,1)(0,0,2)[12] with drift : 3111.139 ARIMA(1,1,1)(1,0,0)[12] : 3111.874 ARIMA(1,1,1)(1,0,0)[12] with drift : 3113.61 ARIMA(1,1,1)(1,0,1)[12] : Inf ARIMA(1,1,1)(1,0,1)[12] with drift : Inf ARIMA(1,1,1)(1,0,2)[12] : Inf ARIMA(1,1,1)(1,0,2)[12] with drift : Inf ARIMA(1,1,1)(2,0,0)[12] : 3113.181 ARIMA(1,1,1)(2,0,0)[12] with drift : 3114.944 ARIMA(1,1,1)(2,0,1)[12] : Inf ARIMA(1,1,1)(2,0,1)[12] with drift : Inf ARIMA(1,1,2) : 3129.316 ARIMA(1,1,2) with drift : 3130.953 ARIMA(1,1,2)(0,0,1)[12] : 3117.513 ARIMA(1,1,2)(0,0,1)[12] with drift : 3119.313 ARIMA(1,1,2)(0,0,2)[12] : 3111.201 ARIMA(1,1,2)(0,0,2)[12] with drift : 3113.025 ARIMA(1,1,2)(1,0,0)[12] : 3113.703 ARIMA(1,1,2)(1,0,0)[12] with drift : 3115.39 ARIMA(1,1,2)(1,0,1)[12] : Inf ARIMA(1,1,2)(1,0,1)[12] with drift : Inf ARIMA(1,1,2)(2,0,0)[12] : 3114.993 ARIMA(1,1,2)(2,0,0)[12] with drift : 3116.706 ARIMA(1,1,3) : 3125.364 ARIMA(1,1,3) with drift : 3126.852 ARIMA(1,1,3)(0,0,1)[12] : 3112.987 ARIMA(1,1,3)(0,0,1)[12] with drift : 3114.59 ARIMA(1,1,3)(1,0,0)[12] : 3109.521 ARIMA(1,1,3)(1,0,0)[12] with drift : 3110.98 ARIMA(1,1,4) : 3126.859 ARIMA(1,1,4) with drift : 3128.277 ARIMA(2,1,0) : 3156.71 ARIMA(2,1,0) with drift : 3158.725 ARIMA(2,1,0)(0,0,1)[12] : 3136.907 ARIMA(2,1,0)(0,0,1)[12] with drift : 3138.943 ARIMA(2,1,0)(0,0,2)[12] : 3132.097 ARIMA(2,1,0)(0,0,2)[12] with drift : 3134.141 ARIMA(2,1,0)(1,0,0)[12] : 3126.481 ARIMA(2,1,0)(1,0,0)[12] with drift : 3128.549 ARIMA(2,1,0)(1,0,1)[12] : Inf ARIMA(2,1,0)(1,0,1)[12] with drift : Inf ARIMA(2,1,0)(1,0,2)[12] : Inf ARIMA(2,1,0)(1,0,2)[12] with drift : Inf ARIMA(2,1,0)(2,0,0)[12] : 3129.669 ARIMA(2,1,0)(2,0,0)[12] with drift : 3131.74 ARIMA(2,1,0)(2,0,1)[12] : Inf ARIMA(2,1,0)(2,0,1)[12] with drift : Inf ARIMA(2,1,1) : 3123.856 ARIMA(2,1,1) with drift : 3125.479 ARIMA(2,1,1)(0,0,1)[12] : 3109.51 ARIMA(2,1,1)(0,0,1)[12] with drift : 3111.24 ARIMA(2,1,1)(0,0,2)[12] : 3105.398 ARIMA(2,1,1)(0,0,2)[12] with drift : 3107.135 ARIMA(2,1,1)(1,0,0)[12] : 3111.809 ARIMA(2,1,1)(1,0,0)[12] with drift : 3113.19 ARIMA(2,1,1)(1,0,1)[12] : Inf ARIMA(2,1,1)(1,0,1)[12] with drift : Inf ARIMA(2,1,1)(2,0,0)[12] : 3118.412 ARIMA(2,1,1)(2,0,0)[12] with drift : 3120.142 ARIMA(2,1,2) : 3125.515 ARIMA(2,1,2) with drift : 3127.079 ARIMA(2,1,2)(0,0,1)[12] : Inf ARIMA(2,1,2)(0,0,1)[12] with drift : Inf ARIMA(2,1,2)(1,0,0)[12] : 3113.878 ARIMA(2,1,2)(1,0,0)[12] with drift : 3115.281 ARIMA(2,1,3) : 3127.311 ARIMA(2,1,3) with drift : 3128.82 ARIMA(3,1,0) : 3154.761 ARIMA(3,1,0) with drift : 3156.761 ARIMA(3,1,0)(0,0,1)[12] : 3135.46 ARIMA(3,1,0)(0,0,1)[12] with drift : 3137.482 ARIMA(3,1,0)(0,0,2)[12] : 3129.146 ARIMA(3,1,0)(0,0,2)[12] with drift : 3131.169 ARIMA(3,1,0)(1,0,0)[12] : 3125.889 ARIMA(3,1,0)(1,0,0)[12] with drift : 3127.97 ARIMA(3,1,0)(1,0,1)[12] : Inf ARIMA(3,1,0)(1,0,1)[12] with drift : Inf ARIMA(3,1,0)(2,0,0)[12] : 3127.238 ARIMA(3,1,0)(2,0,0)[12] with drift : 3129.302 ARIMA(3,1,1) : 3128.525 ARIMA(3,1,1) with drift : 3129.79 ARIMA(3,1,1)(0,0,1)[12] : 3109.761 ARIMA(3,1,1)(0,0,1)[12] with drift : Inf ARIMA(3,1,1)(1,0,0)[12] : Inf ARIMA(3,1,1)(1,0,0)[12] with drift : Inf ARIMA(3,1,2) : 3128.865 ARIMA(3,1,2) with drift : 3130.242 ARIMA(4,1,0) : 3150.852 ARIMA(4,1,0) with drift : 3152.825 ARIMA(4,1,0)(0,0,1)[12] : 3134.169 ARIMA(4,1,0)(0,0,1)[12] with drift : 3136.199 ARIMA(4,1,0)(1,0,0)[12] : 3124.297 ARIMA(4,1,0)(1,0,0)[12] with drift : 3126.393 ARIMA(4,1,1) : 3129.882 ARIMA(4,1,1) with drift : 3131.312 ARIMA(5,1,0) : 3146.938 ARIMA(5,1,0) with drift : 3148.96
Now re-fitting the best model(s) without approximations…
Best model: ARIMA(2,1,1)(0,0,2)[12]
Series: ts_monthly ARIMA(2,1,1)(0,0,2)[12]
Coefficients: ar1 ar2 ma1 sma1 sma2 0.3127 0.2151 -0.9549 0.2564 0.1379 s.e. 0.0777 0.0771 0.0316 0.0745 0.0666
sigma^2 = 2291: log likelihood = -1579.44 AIC=3170.87 AICc=3171.16 BIC=3193.08
Training set error measures: ME RMSE MAE MPE MAPE MASE ACF1 Training
set 5.442304 47.38631 34.60418 0.3967119 8.848714 0.7650856 0.05655193
The ARIMA(2,1,1)(0,0,2)[12] model indicates a seasonal ARIMA with two
autoregressive terms (AR), one differencing step (I), and one moving
average term (MA), alongside two seasonal moving average terms (sMA) for
monthly data. The coefficients provide weights for these components,
with associated standard errors indicating the uncertainty of each
estimate. Key model evaluation metrics include AIC (3170.87), AICc
(3171.16), and BIC (3193.08), where lower values indicate better fit
while penalizing complexity. Training set error measures such as RMSE
(47.39) and MAE (34.60) highlight the average prediction errors. MAPE
(8.85%) reflects a reasonably accurate model, with residuals showing
minimal autocorrelation (ACF1 = 0.056), suggesting a good fit for the
data with little remaining structure in the errors.
The
randomness in the residuals suggest a good fit.[1] “Ljung-Box Test
Results:”
Box-Ljung testdata: ts_monthly_arima_residuals X-squared = 20.077, df = 20, p-value = 0.4531
The residuals do not show significant autocorrelation, indicating
that the ARIMA model has captured the dependencies in the data well, and
no major patterns remain unexplained. [1] “Residual Statistics:” Metric
Value 1 Mean 5.442304 2 Variance 2223.254526 3 Standard Deviation
47.151400
Method RMSE 1 Naive 55.75517 2 SES 49.67305 3 HW 42.96673 4 MA3 28.69516
5 MA6 31.16097 6 MA9 35.25139
Processing category: Larceny
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 2641.64 ARIMA(0,1,0) with drift : 2776.66 ARIMA(1,1,0)(1,0,0)[12] with drift : 2683.655 ARIMA(0,1,1)(0,0,1)[12] with drift : 2709.827 ARIMA(0,1,0) : 2774.658 ARIMA(2,1,2)(0,0,1)[12] with drift : Inf ARIMA(2,1,2)(1,0,0)[12] with drift : 2639.555 ARIMA(2,1,2) with drift : 2649.891 ARIMA(2,1,2)(2,0,0)[12] with drift : 2639.948 ARIMA(2,1,2)(2,0,1)[12] with drift : 2637.192 ARIMA(2,1,2)(2,0,2)[12] with drift : Inf ARIMA(2,1,2)(1,0,2)[12] with drift : 2640.357 ARIMA(1,1,2)(2,0,1)[12] with drift : 2636.174 ARIMA(1,1,2)(1,0,1)[12] with drift : 2640.009 ARIMA(1,1,2)(2,0,0)[12] with drift : 2638.745 ARIMA(1,1,2)(2,0,2)[12] with drift : Inf ARIMA(1,1,2)(1,0,0)[12] with drift : 2638.197 ARIMA(1,1,2)(1,0,2)[12] with drift : 2639.592 ARIMA(0,1,2)(2,0,1)[12] with drift : 2643.392 ARIMA(1,1,1)(2,0,1)[12] with drift : 2634.087 ARIMA(1,1,1)(1,0,1)[12] with drift : 2638.027 ARIMA(1,1,1)(2,0,0)[12] with drift : 2636.886 ARIMA(1,1,1)(2,0,2)[12] with drift : Inf ARIMA(1,1,1)(1,0,0)[12] with drift : 2636.14 ARIMA(1,1,1)(1,0,2)[12] with drift : 2637.483 ARIMA(0,1,1)(2,0,1)[12] with drift : 2642.964 ARIMA(1,1,0)(2,0,1)[12] with drift : 2679.545 ARIMA(2,1,1)(2,0,1)[12] with drift : 2636.359 ARIMA(0,1,0)(2,0,1)[12] with drift : 2745.633 ARIMA(2,1,0)(2,0,1)[12] with drift : 2669.133 ARIMA(1,1,1)(2,0,1)[12] : 2632.422 ARIMA(1,1,1)(1,0,1)[12] : 2636.08 ARIMA(1,1,1)(2,0,0)[12] : 2634.995 ARIMA(1,1,1)(2,0,2)[12] : Inf ARIMA(1,1,1)(1,0,0)[12] : 2634.193 ARIMA(1,1,1)(1,0,2)[12] : 2635.513 ARIMA(0,1,1)(2,0,1)[12] : 2640.881 ARIMA(1,1,0)(2,0,1)[12] : 2677.474 ARIMA(2,1,1)(2,0,1)[12] : 2634.796 ARIMA(1,1,2)(2,0,1)[12] : 2634.476 ARIMA(0,1,0)(2,0,1)[12] : 2743.635 ARIMA(0,1,2)(2,0,1)[12] : 2641.295 ARIMA(2,1,0)(2,0,1)[12] : 2667.037 ARIMA(2,1,2)(2,0,1)[12] : 2635.575
Now re-fitting the best model(s) without approximations…
ARIMA(1,1,1)(2,0,1)[12] : Inf ARIMA(1,1,1)(2,0,1)[12] with drift : Inf ARIMA(1,1,1)(1,0,0)[12] : 2683.859
Best model: ARIMA(1,1,1)(1,0,0)[12]
Ljung-Box
Test p-value for Larceny - Naive Forecast : 1.527187e-06
Ljung-Box
Test p-value for Larceny - Mean Forecast : 0
Ljung-Box
Test p-value for Larceny - Holt-Winters Forecast : 0.1010496
Ljung-Box
Test p-value for Larceny - ARIMA Forecast : 0.1524402
Ljung-Box
Test p-value for STL Residuals: Larceny : 0.001478226 Processing
category: Vandalism
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : Inf ARIMA(0,1,0) with drift : 2332.59 ARIMA(1,1,0)(1,0,0)[12] with drift : 2261.035 ARIMA(0,1,1)(0,0,1)[12] with drift : 2232.947 ARIMA(0,1,0) : 2330.566 ARIMA(0,1,1) with drift : 2237.802 ARIMA(0,1,1)(1,0,1)[12] with drift : 2206.932 ARIMA(0,1,1)(1,0,0)[12] with drift : 2213.167 ARIMA(0,1,1)(2,0,1)[12] with drift : 2198.024 ARIMA(0,1,1)(2,0,0)[12] with drift : 2196.375 ARIMA(0,1,0)(2,0,0)[12] with drift : 2325.821 ARIMA(1,1,1)(2,0,0)[12] with drift : 2195.165 ARIMA(1,1,1)(1,0,0)[12] with drift : 2193.909 ARIMA(1,1,1) with drift : 2205.946 ARIMA(1,1,1)(1,0,1)[12] with drift : 2178.175 ARIMA(1,1,1)(0,0,1)[12] with drift : 2198.938 ARIMA(1,1,1)(2,0,1)[12] with drift : 2196.419 ARIMA(1,1,1)(1,0,2)[12] with drift : 2178.444 ARIMA(1,1,1)(0,0,2)[12] with drift : 2199.567 ARIMA(1,1,1)(2,0,2)[12] with drift : 2192.485 ARIMA(1,1,0)(1,0,1)[12] with drift : 2257.381 ARIMA(2,1,1)(1,0,1)[12] with drift : 2180.963 ARIMA(1,1,2)(1,0,1)[12] with drift : 2180.14 ARIMA(0,1,0)(1,0,1)[12] with drift : 2328.577 ARIMA(0,1,2)(1,0,1)[12] with drift : 2202.586 ARIMA(2,1,0)(1,0,1)[12] with drift : 2227.003 ARIMA(1,1,1)(1,0,1)[12] : 2178.86
Now re-fitting the best model(s) without approximations…
ARIMA(1,1,1)(1,0,1)[12] with drift : Inf ARIMA(1,1,1)(1,0,2)[12] with drift : Inf ARIMA(1,1,1)(1,0,1)[12] : Inf ARIMA(1,1,2)(1,0,1)[12] with drift : 2219.14
Best model: ARIMA(1,1,2)(1,0,1)[12] with drift
Ljung-Box
Test p-value for Vandalism - Naive Forecast : 2.482997e-08
Ljung-Box
Test p-value for Vandalism - Mean Forecast : 0
Ljung-Box
Test p-value for Vandalism - Holt-Winters Forecast : 0.9007833
Ljung-Box
Test p-value for Vandalism - ARIMA Forecast : 0.9190618
Ljung-Box
Test p-value for STL Residuals: Vandalism : 0.09399927 Processing
category: Forgery
Fitting models using approximations to speed things up…
ARIMA(2,0,2)(1,0,1)[12] with non-zero mean : 1633.015 ARIMA(0,0,0) with non-zero mean : 1801.16 ARIMA(1,0,0)(1,0,0)[12] with non-zero mean : 1625.413 ARIMA(0,0,1)(0,0,1)[12] with non-zero mean : 1687.632 ARIMA(0,0,0) with zero mean : 2039.029 ARIMA(1,0,0) with non-zero mean : 1638.37 ARIMA(1,0,0)(2,0,0)[12] with non-zero mean : 1631.362 ARIMA(1,0,0)(1,0,1)[12] with non-zero mean : 1627.392 ARIMA(1,0,0)(0,0,1)[12] with non-zero mean : 1640.343 ARIMA(1,0,0)(2,0,1)[12] with non-zero mean : 1632.356 ARIMA(0,0,0)(1,0,0)[12] with non-zero mean : 1788.799 ARIMA(2,0,0)(1,0,0)[12] with non-zero mean : 1627.932 ARIMA(1,0,1)(1,0,0)[12] with non-zero mean : 1627.368 ARIMA(0,0,1)(1,0,0)[12] with non-zero mean : 1678.182 ARIMA(2,0,1)(1,0,0)[12] with non-zero mean : 1630.024 ARIMA(1,0,0)(1,0,0)[12] with zero mean : 1655.583
Now re-fitting the best model(s) without approximations…
ARIMA(1,0,0)(1,0,0)[12] with non-zero mean : 1639.918
Best model: ARIMA(1,0,0)(1,0,0)[12] with non-zero mean
Ljung-Box
Test p-value for Forgery - Naive Forecast : 0.07279791
Ljung-Box
Test p-value for Forgery - Mean Forecast : 0
Ljung-Box
Test p-value for Forgery - Holt-Winters Forecast : 0.9515707
Ljung-Box
Test p-value for Forgery - ARIMA Forecast : 0.9967535
Ljung-Box
Test p-value for STL Residuals: Forgery : 0.01603712 Processing
category: Simple Assault
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1958.233 ARIMA(0,1,0) with drift : 2113.539 ARIMA(1,1,0)(1,0,0)[12] with drift : 2022.612 ARIMA(0,1,1)(0,0,1)[12] with drift : 1954.714 ARIMA(0,1,0) : 2111.533 ARIMA(0,1,1) with drift : 1952.66 ARIMA(0,1,1)(1,0,0)[12] with drift : 1956.031 ARIMA(0,1,1)(1,0,1)[12] with drift : 1953.576 ARIMA(1,1,1) with drift : 1955.487 ARIMA(0,1,2) with drift : 1954.518 ARIMA(1,1,0) with drift : 2020.182 ARIMA(1,1,2) with drift : 1956.568 ARIMA(0,1,1) : 1950.827 ARIMA(0,1,1)(1,0,0)[12] : 1954.109 ARIMA(0,1,1)(0,0,1)[12] : 1952.868 ARIMA(0,1,1)(1,0,1)[12] : 1951.571 ARIMA(1,1,1) : 1953.46 ARIMA(0,1,2) : 1952.679 ARIMA(1,1,0) : 2018.16 ARIMA(1,1,2) : 1954.571
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1) : 1955.386
Best model: ARIMA(0,1,1)
Ljung-Box
Test p-value for Simple Assault - Naive Forecast : 6.505907e-14
Ljung-Box
Test p-value for Simple Assault - Mean Forecast : 0
Ljung-Box
Test p-value for Simple Assault - Holt-Winters Forecast : 0.8592693
Ljung-Box
Test p-value for Simple Assault - ARIMA Forecast : 0.5248824 Ljung-Box
Test p-value for STL Residuals: Simple Assault : 0.003914289 Processing
category: Burglary
## Warning in HoltWinters(ts_category): optimization difficulties: ERROR:
## ABNORMAL_TERMINATION_IN_LNSRCH
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 2108.454 ARIMA(0,1,0) with drift : 2231.45 ARIMA(1,1,0)(1,0,0)[12] with drift : 2157.879 ARIMA(0,1,1)(0,0,1)[12] with drift : 2109.538 ARIMA(0,1,0) : 2229.433 ARIMA(2,1,2)(0,0,1)[12] with drift : 2106.862 ARIMA(2,1,2) with drift : 2109.407 ARIMA(2,1,2)(0,0,2)[12] with drift : 2100.158 ARIMA(2,1,2)(1,0,2)[12] with drift : 2088.488 ARIMA(2,1,2)(2,0,2)[12] with drift : 2101.188 ARIMA(2,1,2)(2,0,1)[12] with drift : 2100.917 ARIMA(1,1,2)(1,0,2)[12] with drift : 2104.972 ARIMA(2,1,1)(1,0,2)[12] with drift : 2089.891 ARIMA(3,1,2)(1,0,2)[12] with drift : 2104.274 ARIMA(2,1,3)(1,0,2)[12] with drift : Inf ARIMA(1,1,1)(1,0,2)[12] with drift : 2115.62 ARIMA(1,1,3)(1,0,2)[12] with drift : 2101.315 ARIMA(3,1,1)(1,0,2)[12] with drift : 2103.308 ARIMA(3,1,3)(1,0,2)[12] with drift : Inf ARIMA(2,1,2)(1,0,2)[12] : 2089.12
Now re-fitting the best model(s) without approximations…
ARIMA(2,1,2)(1,0,2)[12] with drift : 2100.016
Best model: ARIMA(2,1,2)(1,0,2)[12] with drift
Ljung-Box
Test p-value for Burglary - Naive Forecast : 8.570922e-14
Ljung-Box
Test p-value for Burglary - Mean Forecast : 0
Ljung-Box
Test p-value for Burglary - Holt-Winters Forecast : 0.01535463
Ljung-Box
Test p-value for Burglary - ARIMA Forecast : 0.762681
Ljung-Box
Test p-value for STL Residuals: Burglary : 3.810994e-06 Processing
category: Fraud
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 2113.328 ARIMA(0,1,0) with drift : 2220.713 ARIMA(1,1,0)(1,0,0)[12] with drift : 2174.969 ARIMA(0,1,1)(0,0,1)[12] with drift : 2100.989 ARIMA(0,1,0) : 2218.688 ARIMA(0,1,1) with drift : 2100.173 ARIMA(0,1,1)(1,0,0)[12] with drift : 2107.186 ARIMA(0,1,1)(1,0,1)[12] with drift : 2109.114 ARIMA(1,1,1) with drift : 2101.461 ARIMA(0,1,2) with drift : 2100.544 ARIMA(1,1,0) with drift : 2167.27 ARIMA(1,1,2) with drift : 2103.235 ARIMA(0,1,1) : 2099.778 ARIMA(0,1,1)(1,0,0)[12] : 2105.895 ARIMA(0,1,1)(0,0,1)[12] : 2100.431 ARIMA(0,1,1)(1,0,1)[12] : 2107.876 ARIMA(1,1,1) : 2101.172 ARIMA(0,1,2) : 2100.298 ARIMA(1,1,0) : 2165.273 ARIMA(1,1,2) : 2102.898
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1) : 2105.206
Best model: ARIMA(0,1,1)
Ljung-Box
Test p-value for Fraud - Naive Forecast : 3.019938e-08
Ljung-Box
Test p-value for Fraud - Mean Forecast : 0
Ljung-Box
Test p-value for Fraud - Holt-Winters Forecast : 0.786637
Ljung-Box
Test p-value for Fraud - ARIMA Forecast : 0.7715797
Ljung-Box
Test p-value for STL Residuals: Fraud : 0.02391738 Processing category:
All Other Offenses
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : Inf ARIMA(0,1,0) with drift : 2365.74 ARIMA(1,1,0)(1,0,0)[12] with drift : 2303.053 ARIMA(0,1,1)(0,0,1)[12] with drift : 2248.968 ARIMA(0,1,0) : 2363.713 ARIMA(0,1,1) with drift : 2248.692 ARIMA(0,1,1)(1,0,0)[12] with drift : 2257.24 ARIMA(0,1,1)(1,0,1)[12] with drift : 2252.381 ARIMA(1,1,1) with drift : 2252.277 ARIMA(0,1,2) with drift : 2250.517 ARIMA(1,1,0) with drift : 2294.209 ARIMA(1,1,2) with drift : 2249.89 ARIMA(0,1,1) : 2246.888 ARIMA(0,1,1)(1,0,0)[12] : 2255.337 ARIMA(0,1,1)(0,0,1)[12] : 2247.113 ARIMA(0,1,1)(1,0,1)[12] : 2250.313 ARIMA(1,1,1) : 2250.351 ARIMA(0,1,2) : 2248.72 ARIMA(1,1,0) : 2292.171 ARIMA(1,1,2) : 2248.005
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1) : 2252.451
Best model: ARIMA(0,1,1)
Ljung-Box
Test p-value for All Other Offenses - Naive Forecast : 1.627309e-11
Ljung-Box
Test p-value for All Other Offenses - Mean Forecast : 0
Ljung-Box
Test p-value for All Other Offenses - Holt-Winters Forecast : 0.6371575
Ljung-Box
Test p-value for All Other Offenses - ARIMA Forecast : 0.4050735
Ljung-Box
Test p-value for STL Residuals: All Other Offenses : 0.02077459
Processing category: Drugs
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 2036.727 ARIMA(0,1,0) with drift : 2135.05 ARIMA(1,1,0)(1,0,0)[12] with drift : 2079.031 ARIMA(0,1,1)(0,0,1)[12] with drift : 2026.478 ARIMA(0,1,0) : 2133.022 ARIMA(0,1,1) with drift : 2025.643 ARIMA(0,1,1)(1,0,0)[12] with drift : 2034.695 ARIMA(0,1,1)(1,0,1)[12] with drift : 2035.297 ARIMA(1,1,1) with drift : 2026.898 ARIMA(0,1,2) with drift : 2024.925 ARIMA(0,1,2)(1,0,0)[12] with drift : 2032.814 ARIMA(0,1,2)(0,0,1)[12] with drift : 2025.027 ARIMA(0,1,2)(1,0,1)[12] with drift : 2033.065 ARIMA(1,1,2) with drift : 2028.947 ARIMA(0,1,3) with drift : 2024.874 ARIMA(0,1,3)(1,0,0)[12] with drift : 2032.714 ARIMA(0,1,3)(0,0,1)[12] with drift : 2024.82 ARIMA(0,1,3)(1,0,1)[12] with drift : 2033.141 ARIMA(0,1,3)(0,0,2)[12] with drift : 2026.25 ARIMA(0,1,3)(1,0,2)[12] with drift : 2035.035 ARIMA(1,1,3)(0,0,1)[12] with drift : 2028.703 ARIMA(0,1,4)(0,0,1)[12] with drift : 2026.474 ARIMA(1,1,2)(0,0,1)[12] with drift : 2028.794 ARIMA(1,1,4)(0,0,1)[12] with drift : 2029.596 ARIMA(0,1,3)(0,0,1)[12] : 2022.988 ARIMA(0,1,3) : 2023.072 ARIMA(0,1,3)(1,0,1)[12] : 2031.341 ARIMA(0,1,3)(0,0,2)[12] : 2024.41 ARIMA(0,1,3)(1,0,0)[12] : 2030.959 ARIMA(0,1,3)(1,0,2)[12] : 2033.225 ARIMA(0,1,2)(0,0,1)[12] : 2023.173 ARIMA(1,1,3)(0,0,1)[12] : 2026.757 ARIMA(0,1,4)(0,0,1)[12] : 2024.642 ARIMA(1,1,2)(0,0,1)[12] : 2026.824 ARIMA(1,1,4)(0,0,1)[12] : 2027.661
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,3)(0,0,1)[12] : 2028.217
Best model: ARIMA(0,1,3)(0,0,1)[12]
Ljung-Box
Test p-value for Drugs - Naive Forecast : 5.70779e-11
Ljung-Box
Test p-value for Drugs - Mean Forecast : 0
Ljung-Box
Test p-value for Drugs - Holt-Winters Forecast : 0.05942824
Ljung-Box
Test p-value for Drugs - ARIMA Forecast : 0.3266919
Ljung-Box
Test p-value for STL Residuals: Drugs : 3.092142e-06 Processing
category: Missing Person
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1233.49 ARIMA(0,1,0) with drift : 1356.371 ARIMA(1,1,0)(1,0,0)[12] with drift : 1284.82 ARIMA(0,1,1)(0,0,1)[12] with drift : 1237.582 ARIMA(0,1,0) : 1354.361 ARIMA(2,1,2)(0,0,1)[12] with drift : Inf ARIMA(2,1,2)(1,0,0)[12] with drift : 1231.581 ARIMA(2,1,2) with drift : Inf ARIMA(2,1,2)(2,0,0)[12] with drift : Inf ARIMA(2,1,2)(2,0,1)[12] with drift : Inf ARIMA(1,1,2)(1,0,0)[12] with drift : Inf ARIMA(2,1,1)(1,0,0)[12] with drift : 1232.286 ARIMA(3,1,2)(1,0,0)[12] with drift : 1230.621 ARIMA(3,1,2) with drift : 1228.419 ARIMA(3,1,2)(0,0,1)[12] with drift : Inf ARIMA(3,1,2)(1,0,1)[12] with drift : 1232.706 ARIMA(3,1,1) with drift : 1230.742 ARIMA(4,1,2) with drift : 1224.156 ARIMA(4,1,2)(1,0,0)[12] with drift : 1232.629 ARIMA(4,1,2)(0,0,1)[12] with drift : 1225.037 ARIMA(4,1,2)(1,0,1)[12] with drift : 1231.606 ARIMA(4,1,1) with drift : 1222.09 ARIMA(4,1,1)(1,0,0)[12] with drift : 1230.498 ARIMA(4,1,1)(0,0,1)[12] with drift : 1222.934 ARIMA(4,1,1)(1,0,1)[12] with drift : 1230.422 ARIMA(4,1,0) with drift : 1230.514 ARIMA(5,1,1) with drift : 1225.051 ARIMA(3,1,0) with drift : 1253.004 ARIMA(5,1,0) with drift : 1223.072 ARIMA(5,1,2) with drift : Inf ARIMA(4,1,1) : 1219.997 ARIMA(4,1,1)(1,0,0)[12] : 1228.402 ARIMA(4,1,1)(0,0,1)[12] : 1220.824 ARIMA(4,1,1)(1,0,1)[12] : 1228.289 ARIMA(3,1,1) : 1228.767 ARIMA(4,1,0) : 1228.44 ARIMA(5,1,1) : 1222.949 ARIMA(4,1,2) : 1222.049 ARIMA(3,1,0) : 1250.958 ARIMA(3,1,2) : 1226.467 ARIMA(5,1,0) : 1220.987 ARIMA(5,1,2) : Inf
Now re-fitting the best model(s) without approximations…
ARIMA(4,1,1) : 1230.212
Best model: ARIMA(4,1,1)
Ljung-Box
Test p-value for Missing Person - Naive Forecast : 1.607603e-12
Ljung-Box
Test p-value for Missing Person - Mean Forecast : 0
Ljung-Box
Test p-value for Missing Person - Holt-Winters Forecast : 0.0189024
Ljung-Box
Test p-value for Missing Person - ARIMA Forecast : 0.3000926
Ljung-Box
Test p-value for STL Residuals: Missing Person : 0.000183457 Processing
category: Motor Vehicle Theft
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1703.658 ARIMA(0,1,0) with drift : 1805.419 ARIMA(1,1,0)(1,0,0)[12] with drift : 1736.452 ARIMA(0,1,1)(0,0,1)[12] with drift : 1708.727 ARIMA(0,1,0) : 1803.394 ARIMA(2,1,2)(0,0,1)[12] with drift : 1711.618 ARIMA(2,1,2)(1,0,0)[12] with drift : 1705.231 ARIMA(2,1,2)(2,0,1)[12] with drift : 1703.142 ARIMA(2,1,2)(2,0,0)[12] with drift : 1702.686 ARIMA(1,1,2)(2,0,0)[12] with drift : 1703.437 ARIMA(2,1,1)(2,0,0)[12] with drift : 1700.583 ARIMA(2,1,1)(1,0,0)[12] with drift : 1704.421 ARIMA(2,1,1)(2,0,1)[12] with drift : 1701.033 ARIMA(2,1,1)(1,0,1)[12] with drift : 1704.269 ARIMA(1,1,1)(2,0,0)[12] with drift : 1701.948 ARIMA(2,1,0)(2,0,0)[12] with drift : 1709.634 ARIMA(3,1,1)(2,0,0)[12] with drift : 1698.399 ARIMA(3,1,1)(1,0,0)[12] with drift : 1709.438 ARIMA(3,1,1)(2,0,1)[12] with drift : 1700.494 ARIMA(3,1,1)(1,0,1)[12] with drift : 1706.779 ARIMA(3,1,0)(2,0,0)[12] with drift : 1709.962 ARIMA(4,1,1)(2,0,0)[12] with drift : 1703.331 ARIMA(3,1,2)(2,0,0)[12] with drift : 1699.469 ARIMA(4,1,0)(2,0,0)[12] with drift : 1711.704 ARIMA(4,1,2)(2,0,0)[12] with drift : 1703.954 ARIMA(3,1,1)(2,0,0)[12] : 1696.935 ARIMA(3,1,1)(1,0,0)[12] : 1707.343 ARIMA(3,1,1)(2,0,1)[12] : 1699.035 ARIMA(3,1,1)(1,0,1)[12] : 1704.673 ARIMA(2,1,1)(2,0,0)[12] : 1698.604 ARIMA(3,1,0)(2,0,0)[12] : 1707.893 ARIMA(4,1,1)(2,0,0)[12] : 1701.831 ARIMA(3,1,2)(2,0,0)[12] : 1697.918 ARIMA(2,1,0)(2,0,0)[12] : 1707.565 ARIMA(2,1,2)(2,0,0)[12] : 1700.685 ARIMA(4,1,0)(2,0,0)[12] : 1709.644 ARIMA(4,1,2)(2,0,0)[12] : 1702.471
Now re-fitting the best model(s) without approximations…
ARIMA(3,1,1)(2,0,0)[12] : 1709.192
Best model: ARIMA(3,1,1)(2,0,0)[12]
Ljung-Box
Test p-value for Motor Vehicle Theft - Naive Forecast : 5.401332e-07
Ljung-Box
Test p-value for Motor Vehicle Theft - Mean Forecast : 0
Ljung-Box
Test p-value for Motor Vehicle Theft - Holt-Winters Forecast : 0.2059866
Ljung-Box
Test p-value for Motor Vehicle Theft - ARIMA Forecast : 0.9971646
Ljung-Box
Test p-value for STL Residuals: Motor Vehicle Theft : 0.06283549
Processing category:
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1775.655 ARIMA(0,1,0) with drift : 1847.328 ARIMA(1,1,0)(1,0,0)[12] with drift : 1840.079 ARIMA(0,1,1)(0,0,1)[12] with drift : 1797.562 ARIMA(0,1,0) : 1845.302 ARIMA(2,1,2)(0,0,1)[12] with drift : 1766.975 ARIMA(2,1,2) with drift : 1764.925 ARIMA(2,1,2)(1,0,0)[12] with drift : 1773.557 ARIMA(1,1,2) with drift : 1766.05 ARIMA(2,1,1) with drift : 1767.775 ARIMA(3,1,2) with drift : Inf ARIMA(2,1,3) with drift : 1766.966 ARIMA(1,1,1) with drift : 1767.053 ARIMA(1,1,3) with drift : 1768.135 ARIMA(3,1,1) with drift : 1768.799 ARIMA(3,1,3) with drift : Inf ARIMA(2,1,2) : 1764.077 ARIMA(2,1,2)(1,0,0)[12] : 1772.894 ARIMA(2,1,2)(0,0,1)[12] : 1766.121 ARIMA(2,1,2)(1,0,1)[12] : 1774.956 ARIMA(1,1,2) : 1764.978 ARIMA(2,1,1) : 1766.719 ARIMA(3,1,2) : 1766.845 ARIMA(2,1,3) : 1766.025 ARIMA(1,1,1) : 1766.393 ARIMA(1,1,3) : 1767.006 ARIMA(3,1,1) : 1768.048 ARIMA(3,1,3) : 1770.041
Now re-fitting the best model(s) without approximations…
ARIMA(2,1,2) : 1767.102
Best model: ARIMA(2,1,2)
Ljung-Box
Test p-value for - Naive Forecast : 9.617126e-05
Ljung-Box
Test p-value for - Mean Forecast : 0
Ljung-Box
Test p-value for - Holt-Winters Forecast : 0.1314561
Ljung-Box
Test p-value for - ARIMA Forecast : 0.8698869
Ljung-Box
Test p-value for STL Residuals: : 1.265572e-05 Processing category:
Weapons
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1003.524 ARIMA(0,1,0) with drift : 1162.605 ARIMA(1,1,0)(1,0,0)[12] with drift : 1092.086 ARIMA(0,1,1)(0,0,1)[12] with drift : 1025.88 ARIMA(0,1,0) : 1160.588 ARIMA(2,1,2)(0,0,1)[12] with drift : 998.7729 ARIMA(2,1,2) with drift : 996.9786 ARIMA(2,1,2)(1,0,0)[12] with drift : 1001.883 ARIMA(1,1,2) with drift : 994.5858 ARIMA(1,1,2)(1,0,0)[12] with drift : 1002.848 ARIMA(1,1,2)(0,0,1)[12] with drift : 996.2263 ARIMA(1,1,2)(1,0,1)[12] with drift : 1002.23 ARIMA(0,1,2) with drift : 1025.601 ARIMA(1,1,1) with drift : 992.578 ARIMA(1,1,1)(1,0,0)[12] with drift : 1000.902 ARIMA(1,1,1)(0,0,1)[12] with drift : 994.2099 ARIMA(1,1,1)(1,0,1)[12] with drift : 1002.827 ARIMA(0,1,1) with drift : 1024.115 ARIMA(1,1,0) with drift : 1087.093 ARIMA(2,1,1) with drift : 1001.741 ARIMA(2,1,0) with drift : 1048.814 ARIMA(1,1,1) : 992.7667
Now re-fitting the best model(s) without approximations…
ARIMA(1,1,1) with drift : 1004.528
Best model: ARIMA(1,1,1) with drift
Ljung-Box
Test p-value for Weapons - Naive Forecast : 1.386472e-08
Ljung-Box
Test p-value for Weapons - Mean Forecast : 0
Ljung-Box
Test p-value for Weapons - Holt-Winters Forecast : 0.9054433
Ljung-Box
Test p-value for Weapons - ARIMA Forecast : 0.9017289 Ljung-Box Test
p-value for STL Residuals: Weapons : 0.05359485 Processing category:
Traffic Except DWI
## Warning in HoltWinters(ts_category): optimization difficulties: ERROR:
## ABNORMAL_TERMINATION_IN_LNSRCH
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1580.283 ARIMA(0,1,0) with drift : 1667.695 ARIMA(1,1,0)(1,0,0)[12] with drift : 1612.382 ARIMA(0,1,1)(0,0,1)[12] with drift : 1563.861 ARIMA(0,1,0) : 1665.675 ARIMA(0,1,1) with drift : 1564.065 ARIMA(0,1,1)(1,0,1)[12] with drift : 1576.074 ARIMA(0,1,1)(0,0,2)[12] with drift : 1564.506 ARIMA(0,1,1)(1,0,0)[12] with drift : 1574.247 ARIMA(0,1,1)(1,0,2)[12] with drift : 1576.949 ARIMA(0,1,0)(0,0,1)[12] with drift : 1668.557 ARIMA(1,1,1)(0,0,1)[12] with drift : 1566.512 ARIMA(0,1,2)(0,0,1)[12] with drift : 1565.105 ARIMA(1,1,0)(0,0,1)[12] with drift : 1602.224 ARIMA(1,1,2)(0,0,1)[12] with drift : 1568.282 ARIMA(0,1,1)(0,0,1)[12] : 1562.327 ARIMA(0,1,1) : 1562.457 ARIMA(0,1,1)(1,0,1)[12] : 1574.509 ARIMA(0,1,1)(0,0,2)[12] : 1562.93 ARIMA(0,1,1)(1,0,0)[12] : 1572.679 ARIMA(0,1,1)(1,0,2)[12] : 1575.276 ARIMA(0,1,0)(0,0,1)[12] : 1666.524 ARIMA(1,1,1)(0,0,1)[12] : 1564.987 ARIMA(0,1,2)(0,0,1)[12] : 1563.52 ARIMA(1,1,0)(0,0,1)[12] : 1600.251 ARIMA(1,1,2)(0,0,1)[12] : 1566.702
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1)(0,0,1)[12] : 1566.002
Best model: ARIMA(0,1,1)(0,0,1)[12]
Ljung-Box
Test p-value for Traffic Except DWI - Naive Forecast : 6.126916e-09
Ljung-Box
Test p-value for Traffic Except DWI - Mean Forecast : 0
Ljung-Box
Test p-value for Traffic Except DWI - Holt-Winters Forecast : 0.73422
Ljung-Box
Test p-value for Traffic Except DWI - ARIMA Forecast : 0.8634272
Ljung-Box
Test p-value for STL Residuals: Traffic Except DWI : 0.1191584
Processing category: Aggravated Assault
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1177.156 ARIMA(0,1,0) with drift : 1361.828 ARIMA(1,1,0)(1,0,0)[12] with drift : 1286.102 ARIMA(0,1,1)(0,0,1)[12] with drift : 1166.586 ARIMA(0,1,0) : 1359.802 ARIMA(0,1,1) with drift : 1165.956 ARIMA(0,1,1)(1,0,0)[12] with drift : 1185.043 ARIMA(0,1,1)(1,0,1)[12] with drift : 1183.359 ARIMA(1,1,1) with drift : 1169.105 ARIMA(0,1,2) with drift : 1167.735 ARIMA(1,1,0) with drift : 1279.598 ARIMA(1,1,2) with drift : 1169.528 ARIMA(0,1,1) : 1164.803 ARIMA(0,1,1)(1,0,0)[12] : 1183.678 ARIMA(0,1,1)(0,0,1)[12] : 1165.373 ARIMA(0,1,1)(1,0,1)[12] : 1182.282 ARIMA(1,1,1) : 1168.007 ARIMA(0,1,2) : 1166.431 ARIMA(1,1,0) : 1277.558 ARIMA(1,1,2) : 1168.936
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1) : 1167.382
Best model: ARIMA(0,1,1)
Ljung-Box
Test p-value for Aggravated Assault - Naive Forecast : 1.453305e-10
Ljung-Box
Test p-value for Aggravated Assault - Mean Forecast : 0.04504411
Ljung-Box
Test p-value for Aggravated Assault - Holt-Winters Forecast : 0.773886
Ljung-Box
Test p-value for Aggravated Assault - ARIMA Forecast : 0.7395607
Ljung-Box
Test p-value for STL Residuals: Aggravated Assault : 0.01247429
Processing category: Stolen Property
Fitting models using approximations to speed things up…
ARIMA(2,0,2)(1,0,1)[12] with non-zero mean : 714.1806 ARIMA(0,0,0) with non-zero mean : 711.3391 ARIMA(1,0,0)(1,0,0)[12] with non-zero mean : 711.3097 ARIMA(0,0,1)(0,0,1)[12] with non-zero mean : 714.7307 ARIMA(0,0,0) with zero mean : 1027.13 ARIMA(1,0,0) with non-zero mean : 713.6401 ARIMA(1,0,0)(2,0,0)[12] with non-zero mean : 711.7651 ARIMA(1,0,0)(1,0,1)[12] with non-zero mean : 712.8517 ARIMA(1,0,0)(0,0,1)[12] with non-zero mean : 715.0504 ARIMA(1,0,0)(2,0,1)[12] with non-zero mean : 712.3669 ARIMA(0,0,0)(1,0,0)[12] with non-zero mean : 708.9065 ARIMA(0,0,0)(2,0,0)[12] with non-zero mean : 709.1305 ARIMA(0,0,0)(1,0,1)[12] with non-zero mean : 710.4019 ARIMA(0,0,0)(0,0,1)[12] with non-zero mean : 712.6614 ARIMA(0,0,0)(2,0,1)[12] with non-zero mean : 710.1593 ARIMA(0,0,1)(1,0,0)[12] with non-zero mean : 710.9787 ARIMA(1,0,1)(1,0,0)[12] with non-zero mean : 712.4647 ARIMA(0,0,0)(1,0,0)[12] with zero mean : 826.1549
Now re-fitting the best model(s) without approximations…
ARIMA(0,0,0)(1,0,0)[12] with non-zero mean : 712.5003
Best model: ARIMA(0,0,0)(1,0,0)[12] with non-zero mean
Ljung-Box
Test p-value for Stolen Property - Naive Forecast : 5.844937e-08
Ljung-Box
Test p-value for Stolen Property - Mean Forecast : 0.4597357
Ljung-Box
Test p-value for Stolen Property - Holt-Winters Forecast : 0.7589937
Ljung-Box
Test p-value for Stolen Property - ARIMA Forecast : 0.5038815
Ljung-Box
Test p-value for STL Residuals: Stolen Property : 0.09713705 Processing
category: Alcohol Offenses
Fitting models using approximations to speed things up…
ARIMA(2,0,2)(1,0,1)[12] with non-zero mean : 627.0149 ARIMA(0,0,0) with non-zero mean : 650.9832 ARIMA(1,0,0)(1,0,0)[12] with non-zero mean : 626.2375 ARIMA(0,0,1)(0,0,1)[12] with non-zero mean : 649.8751 ARIMA(0,0,0) with zero mean : 901.3115 ARIMA(1,0,0) with non-zero mean : 647.0568 ARIMA(1,0,0)(2,0,0)[12] with non-zero mean : 635.2371 ARIMA(1,0,0)(1,0,1)[12] with non-zero mean : 628.0333 ARIMA(1,0,0)(0,0,1)[12] with non-zero mean : 648.9856 ARIMA(1,0,0)(2,0,1)[12] with non-zero mean : 635.9113 ARIMA(0,0,0)(1,0,0)[12] with non-zero mean : 632.6926 ARIMA(2,0,0)(1,0,0)[12] with non-zero mean : 623.3495 ARIMA(2,0,0) with non-zero mean : 642.599 ARIMA(2,0,0)(2,0,0)[12] with non-zero mean : 632.8493 ARIMA(2,0,0)(1,0,1)[12] with non-zero mean : 624.7798 ARIMA(2,0,0)(0,0,1)[12] with non-zero mean : 644.6912 ARIMA(2,0,0)(2,0,1)[12] with non-zero mean : 634.7545 ARIMA(3,0,0)(1,0,0)[12] with non-zero mean : 624.2646 ARIMA(2,0,1)(1,0,0)[12] with non-zero mean : 623.4951 ARIMA(1,0,1)(1,0,0)[12] with non-zero mean : 620.6952 ARIMA(1,0,1) with non-zero mean : 641.1887 ARIMA(1,0,1)(2,0,0)[12] with non-zero mean : 629.1078 ARIMA(1,0,1)(1,0,1)[12] with non-zero mean : 621.9377 ARIMA(1,0,1)(0,0,1)[12] with non-zero mean : 643.2829 ARIMA(1,0,1)(2,0,1)[12] with non-zero mean : 631.2013 ARIMA(0,0,1)(1,0,0)[12] with non-zero mean : 628.2296 ARIMA(1,0,2)(1,0,0)[12] with non-zero mean : 622.1069 ARIMA(0,0,2)(1,0,0)[12] with non-zero mean : 625.8714 ARIMA(2,0,2)(1,0,0)[12] with non-zero mean : 625.6268 ARIMA(1,0,1)(1,0,0)[12] with zero mean : Inf
Now re-fitting the best model(s) without approximations…
ARIMA(1,0,1)(1,0,0)[12] with non-zero mean : 642.3412
Best model: ARIMA(1,0,1)(1,0,0)[12] with non-zero mean
Ljung-Box
Test p-value for Alcohol Offenses - Naive Forecast : 7.392966e-07
Ljung-Box
Test p-value for Alcohol Offenses - Mean Forecast : 0.02706037
Ljung-Box
Test p-value for Alcohol Offenses - Holt-Winters Forecast : 0.6155893
Ljung-Box
Test p-value for Alcohol Offenses - ARIMA Forecast : 0.9316562
Ljung-Box
Test p-value for STL Residuals: Alcohol Offenses : 0.2785603 Processing
category: Drunkenness
Fitting models using approximations to speed things up…
ARIMA(2,0,2)(1,0,1)[12] with non-zero mean : 685.354 ARIMA(0,0,0) with non-zero mean : 679.524 ARIMA(1,0,0)(1,0,0)[12] with non-zero mean : 680.934 ARIMA(0,0,1)(0,0,1)[12] with non-zero mean : 674.5013 ARIMA(0,0,0) with zero mean : 980.1668 ARIMA(0,0,1) with non-zero mean : 674.0378 ARIMA(0,0,1)(1,0,0)[12] with non-zero mean : 681.7818 ARIMA(0,0,1)(1,0,1)[12] with non-zero mean : 683.6758 ARIMA(1,0,1) with non-zero mean : 670.7251 ARIMA(1,0,1)(1,0,0)[12] with non-zero mean : 678.9194 ARIMA(1,0,1)(0,0,1)[12] with non-zero mean : 670.2638 ARIMA(1,0,1)(1,0,1)[12] with non-zero mean : 680.0316 ARIMA(1,0,1)(0,0,2)[12] with non-zero mean : 672.1654 ARIMA(1,0,1)(1,0,2)[12] with non-zero mean : 681.9477 ARIMA(1,0,0)(0,0,1)[12] with non-zero mean : 673.4422 ARIMA(2,0,1)(0,0,1)[12] with non-zero mean : 673.0538 ARIMA(1,0,2)(0,0,1)[12] with non-zero mean : 672.1487 ARIMA(0,0,0)(0,0,1)[12] with non-zero mean : 679.2694 ARIMA(0,0,2)(0,0,1)[12] with non-zero mean : 673.9827 ARIMA(2,0,0)(0,0,1)[12] with non-zero mean : 674.22 ARIMA(2,0,2)(0,0,1)[12] with non-zero mean : 675.1838 ARIMA(1,0,1)(0,0,1)[12] with zero mean : Inf
Now re-fitting the best model(s) without approximations…
ARIMA(1,0,1)(0,0,1)[12] with non-zero mean : 671.1076
Best model: ARIMA(1,0,1)(0,0,1)[12] with non-zero mean
Ljung-Box
Test p-value for Drunkenness - Naive Forecast : 2.781361e-08
Ljung-Box
Test p-value for Drunkenness - Mean Forecast : 0.00274216
Ljung-Box
Test p-value for Drunkenness - Holt-Winters Forecast : 0.04449286
Ljung-Box
Test p-value for Drunkenness - ARIMA Forecast : 0.4497937
Ljung-Box
Test p-value for STL Residuals: Drunkenness : 0.0002278958 Processing
category: DUI
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1695.421 ARIMA(0,1,0) with drift : 1761.531 ARIMA(1,1,0)(1,0,0)[12] with drift : 1706.67 ARIMA(0,1,1)(0,0,1)[12] with drift : 1675.868 ARIMA(0,1,0) : 1759.504 ARIMA(0,1,1) with drift : 1678.236 ARIMA(0,1,1)(1,0,1)[12] with drift : 1688.819 ARIMA(0,1,1)(0,0,2)[12] with drift : 1676.91 ARIMA(0,1,1)(1,0,0)[12] with drift : 1686.84 ARIMA(0,1,1)(1,0,2)[12] with drift : 1688.73 ARIMA(0,1,0)(0,0,1)[12] with drift : 1757.175 ARIMA(1,1,1)(0,0,1)[12] with drift : 1677.86 ARIMA(0,1,2)(0,0,1)[12] with drift : 1677.427 ARIMA(1,1,0)(0,0,1)[12] with drift : 1696.446 ARIMA(1,1,2)(0,0,1)[12] with drift : 1679.656 ARIMA(0,1,1)(0,0,1)[12] : 1673.847 ARIMA(0,1,1) : 1676.258 ARIMA(0,1,1)(1,0,1)[12] : 1686.794 ARIMA(0,1,1)(0,0,2)[12] : 1674.866 ARIMA(0,1,1)(1,0,0)[12] : 1684.831 ARIMA(0,1,1)(1,0,2)[12] : 1686.712 ARIMA(0,1,0)(0,0,1)[12] : 1755.132 ARIMA(1,1,1)(0,0,1)[12] : 1675.841 ARIMA(0,1,2)(0,0,1)[12] : 1675.388 ARIMA(1,1,0)(0,0,1)[12] : 1694.398 ARIMA(1,1,2)(0,0,1)[12] : 1677.63
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1)(0,0,1)[12] : 1677.603
Best model: ARIMA(0,1,1)(0,0,1)[12]
Ljung-Box
Test p-value for DUI - Naive Forecast : 3.528362e-10
Ljung-Box
Test p-value for DUI - Mean Forecast : 0
Ljung-Box
Test p-value for DUI - Holt-Winters Forecast : 0.1799627
Ljung-Box
Test p-value for DUI - ARIMA Forecast : 0.2390681
Ljung-Box
Test p-value for STL Residuals: DUI : 0.002544789 Processing category:
Suicide
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : 1291.187 ARIMA(0,1,0) with drift : 1459.012 ARIMA(1,1,0)(1,0,0)[12] with drift : 1384.184 ARIMA(0,1,1)(0,0,1)[12] with drift : 1278.22 ARIMA(0,1,0) : 1456.988 ARIMA(0,1,1) with drift : 1276.825 ARIMA(0,1,1)(1,0,0)[12] with drift : 1279.729 ARIMA(0,1,1)(1,0,1)[12] with drift : 1279.968 ARIMA(1,1,1) with drift : 1282.467 ARIMA(0,1,2) with drift : 1278.88 ARIMA(1,1,0) with drift : 1378.819 ARIMA(1,1,2) with drift : 1278.952 ARIMA(0,1,1) : 1275.03 ARIMA(0,1,1)(1,0,0)[12] : 1277.722 ARIMA(0,1,1)(0,0,1)[12] : 1276.411 ARIMA(0,1,1)(1,0,1)[12] : 1277.909 ARIMA(1,1,1) : 1280.433 ARIMA(0,1,2) : 1277.072 ARIMA(1,1,0) : 1376.779 ARIMA(1,1,2) : 1276.893
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1) : 1276.485
Best model: ARIMA(0,1,1)
Ljung-Box
Test p-value for Suicide - Naive Forecast : 3.306901e-10
Ljung-Box
Test p-value for Suicide - Mean Forecast : 0.0008676618
Ljung-Box
Test p-value for Suicide - Holt-Winters Forecast : 0.9879291
Ljung-Box
Test p-value for Suicide - ARIMA Forecast : 0.9654798
Ljung-Box
Test p-value for STL Residuals: Suicide : 0.1157256 Processing category:
Arson
ARIMA(2,0,2)(1,0,1)[12] with non-zero mean : 281.9897 ARIMA(0,0,0) with non-zero mean : 272.8251 ARIMA(1,0,0)(1,0,0)[12] with non-zero mean : 276.4537 ARIMA(0,0,1)(0,0,1)[12] with non-zero mean : 276.3587 ARIMA(0,0,0) with zero mean : 446.7236 ARIMA(0,0,0)(1,0,0)[12] with non-zero mean : 274.305 ARIMA(0,0,0)(0,0,1)[12] with non-zero mean : 274.2119 ARIMA(0,0,0)(1,0,1)[12] with non-zero mean : 276.2835 ARIMA(1,0,0) with non-zero mean : 274.9216 ARIMA(0,0,1) with non-zero mean : 274.9218 ARIMA(1,0,1) with non-zero mean : 275.7804
Best model: ARIMA(0,0,0) with non-zero mean
Ljung-Box
Test p-value for Arson - Naive Forecast : 0.0001476746
Ljung-Box
Test p-value for Arson - Mean Forecast : 0.2801111
Ljung-Box
Test p-value for Arson - Holt-Winters Forecast : 0.5006736
Ljung-Box
Test p-value for Arson - ARIMA Forecast : 0.2801111
Ljung-Box
Test p-value for STL Residuals: Arson : 0.05347482 Processing category:
Embezzlement
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : Inf ARIMA(0,1,0) with drift : 1256.522 ARIMA(1,1,0)(1,0,0)[12] with drift : 1166.802 ARIMA(0,1,1)(0,0,1)[12] with drift : 1083.445 ARIMA(0,1,0) : 1254.494 ARIMA(0,1,1) with drift : 1081.682 ARIMA(0,1,1)(1,0,0)[12] with drift : 1065.678 ARIMA(0,1,1)(2,0,0)[12] with drift : 1060.513 ARIMA(0,1,1)(2,0,1)[12] with drift : Inf ARIMA(0,1,1)(1,0,1)[12] with drift : Inf ARIMA(0,1,0)(2,0,0)[12] with drift : 1247.022 ARIMA(1,1,1)(2,0,0)[12] with drift : 1064.631 ARIMA(0,1,2)(2,0,0)[12] with drift : 1060.997 ARIMA(1,1,0)(2,0,0)[12] with drift : 1166.883 ARIMA(1,1,2)(2,0,0)[12] with drift : 1066.862 ARIMA(0,1,1)(2,0,0)[12] : 1061.268
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1)(2,0,0)[12] with drift : Inf ARIMA(0,1,2)(2,0,0)[12] with drift : Inf ARIMA(0,1,1)(2,0,0)[12] : 1077.052
Best model: ARIMA(0,1,1)(2,0,0)[12]
Ljung-Box
Test p-value for Embezzlement - Naive Forecast : 1.563849e-11
Ljung-Box
Test p-value for Embezzlement - Mean Forecast : 0
Ljung-Box
Test p-value for Embezzlement - Holt-Winters Forecast : 0.7276434
Ljung-Box
Test p-value for Embezzlement - ARIMA Forecast : 0.5963342
Ljung-Box
Test p-value for STL Residuals: Embezzlement : 0.02397306 Processing
category: Disorderly Conduct
Fitting models using approximations to speed things up…
ARIMA(2,1,2)(1,0,1)[12] with drift : Inf ARIMA(0,1,0) with drift : 819.5349 ARIMA(1,1,0)(1,0,0)[12] with drift : 766.5201 ARIMA(0,1,1)(0,0,1)[12] with drift : 700.2158 ARIMA(0,1,0) : 817.4989 ARIMA(0,1,1) with drift : 698.1954 ARIMA(0,1,1)(1,0,0)[12] with drift : 705.081 ARIMA(0,1,1)(1,0,1)[12] with drift : 705.1481 ARIMA(1,1,1) with drift : 700.3085 ARIMA(0,1,2) with drift : 699.4031 ARIMA(1,1,0) with drift : 760.4518 ARIMA(1,1,2) with drift : 701.9666 ARIMA(0,1,1) : 696.1994 ARIMA(0,1,1)(1,0,0)[12] : 703.0352 ARIMA(0,1,1)(0,0,1)[12] : 698.2004 ARIMA(0,1,1)(1,0,1)[12] : 703.0692 ARIMA(1,1,1) : 698.2807 ARIMA(0,1,2) : 697.3876 ARIMA(1,1,0) : 758.3982 ARIMA(1,1,2) : 699.9114
Now re-fitting the best model(s) without approximations…
ARIMA(0,1,1) : 695.5634
Best model: ARIMA(0,1,1)
Ljung-Box
Test p-value for Disorderly Conduct - Naive Forecast : 2.631229e-14
Ljung-Box
Test p-value for Disorderly Conduct - Mean Forecast : 0.0005170751
Ljung-Box
Test p-value for Disorderly Conduct - Holt-Winters Forecast : 0.07636961
Ljung-Box
Test p-value for Disorderly Conduct - ARIMA Forecast : 0.06530758
Ljung-Box
Test p-value for STL Residuals: Disorderly Conduct : 0.001545906
Processing category: Pornography
ARIMA(2,0,2)(1,0,1)[12] with non-zero mean : Inf ARIMA(0,0,0) with non-zero mean : 87.43653 ARIMA(1,0,0)(1,0,0)[12] with non-zero mean : 90.56536 ARIMA(0,0,1)(0,0,1)[12] with non-zero mean : 90.5408 ARIMA(0,0,0) with zero mean : 184.6775 ARIMA(0,0,0)(1,0,0)[12] with non-zero mean : 89.59076 ARIMA(0,0,0)(0,0,1)[12] with non-zero mean : 89.62992 ARIMA(0,0,0)(1,0,1)[12] with non-zero mean : Inf ARIMA(1,0,0) with non-zero mean : 88.39065 ARIMA(0,0,1) with non-zero mean : 88.28496 ARIMA(1,0,1) with non-zero mean : Inf
Best model: ARIMA(0,0,0) with non-zero mean
Ljung-Box
Test p-value for Pornography - Naive Forecast : 0.005772429
Ljung-Box
Test p-value for Pornography - Mean Forecast : 0.6229255
Ljung-Box
Test p-value for Pornography - Holt-Winters Forecast : 0.8459962
Ljung-Box
Test p-value for Pornography - ARIMA Forecast : 0.6229255
Ljung-Box
Test p-value for STL Residuals: Pornography : 0.07096858 Processing
category: Murder Insufficient data for STL decomposition for category:
Murder Processing category: Non Negligent Traff Insufficient data for
STL decomposition for category: Non Negligent Traff Processing category:
Gambling Insufficient data for STL decomposition for category: Gambling
Processing category: Calls for Service
ARIMA(2,0,2) with non-zero mean : Inf ARIMA(0,0,0) with non-zero mean : 8.772111 ARIMA(1,0,0) with non-zero mean : 11.13465 ARIMA(0,0,1) with non-zero mean : 11.09062 ARIMA(0,0,0) with zero mean : 84.20079 ARIMA(1,0,1) with non-zero mean : Inf
Best model: ARIMA(0,0,0) with non-zero mean
Ljung-Box
Test p-value for Calls for Service - Naive Forecast : 0.0006768923
Ljung-Box
Test p-value for Calls for Service - Mean Forecast : 0.1919992
Ljung-Box
Test p-value for Calls for Service - Holt-Winters Forecast : NA
Ljung-Box
Test p-value for Calls for Service - ARIMA Forecast : 0.1919992
Ljung-Box
Test p-value for STL Residuals: Calls for Service : 0.004584851
Processing category: Non Criminal Detain
ARIMA(2,1,2) with drift : 199.0386 ARIMA(0,1,0) with drift : 208.4051 ARIMA(1,1,0) with drift : 197.0616 ARIMA(0,1,1) with drift : 196.612 ARIMA(0,1,0) : 206.1629 ARIMA(1,1,1) with drift : 198.1586 ARIMA(0,1,2) with drift : 198.2635 ARIMA(1,1,2) with drift : 196.5745 ARIMA(1,1,3) with drift : 197.847 ARIMA(0,1,3) with drift : 201.0605 ARIMA(2,1,1) with drift : 200.6467 ARIMA(2,1,3) with drift : 198.7708 ARIMA(1,1,2) : 194.3352 ARIMA(0,1,2) : 196.0607 ARIMA(1,1,1) : 196.0295 ARIMA(2,1,2) : 196.7686 ARIMA(1,1,3) : 195.7849 ARIMA(0,1,1) : 194.9304 ARIMA(0,1,3) : 198.3212 ARIMA(2,1,1) : 198.4078 ARIMA(2,1,3) : Inf
Best model: ARIMA(1,1,2)
Ljung-Box
Test p-value for Non Criminal Detain - Naive Forecast : 3.462545e-07
Ljung-Box
Test p-value for Non Criminal Detain - Mean Forecast : 1.180947e-08
Ljung-Box
Test p-value for Non Criminal Detain - Holt-Winters Forecast : 0.3198892
Ljung-Box
Test p-value for Non Criminal Detain - ARIMA Forecast : 0.7445539
Ljung-Box
Test p-value for STL Residuals: Non Criminal Detain : 0.02024312
Processing category: NA Error processing category: NA - no rows to
aggregate Successfully processed categories: Larceny Vandalism Forgery
Simple Assault Burglary Fraud All Other Offenses Drugs Missing Person
Motor Vehicle Theft Weapons Traffic Except DWI Aggravated Assault Stolen
Property Alcohol Offenses Drunkenness DUI Suicide Arson Embezzlement
Disorderly Conduct Pornography Calls for Service Non Criminal Detain
Categories with issues:
RMSE for category: Larceny Naive RMSE: 25.23893 Mean RMSE: 23.41082 Holt-Winters RMSE: 20.45496 STL RMSE: 7.336082 ARIMA RMSE: 21.13999
RMSE for category: Vandalism Naive RMSE: 11.98034 Mean RMSE: 13.5175 Holt-Winters RMSE: 9.69951 STL RMSE: 3.334571 ARIMA RMSE: 9.60029
RMSE for category: Forgery Naive RMSE: 4.284809 Mean RMSE: 5.195624 Holt-Winters RMSE: 4.417228 STL RMSE: 0.5847482 ARIMA RMSE: 3.914415
RMSE for category: Simple Assault Naive RMSE: 8.395229 Mean RMSE: 7.380232 Holt-Winters RMSE: 6.6264 STL RMSE: 1.985979 ARIMA RMSE: 6.365325
RMSE for category: Burglary Naive RMSE: 10.23843 Mean RMSE: 12.20652 Holt-Winters RMSE: 9.02529 STL RMSE: 1.610248 ARIMA RMSE: 7.892439
RMSE for category: Fraud Naive RMSE: 10.05488 Mean RMSE: 10.1406 Holt-Winters RMSE: 8.706708 STL RMSE: 1.635293 ARIMA RMSE: 8.192234
RMSE for category: All Other Offenses Naive RMSE: 12.83543 Mean RMSE: 21.06401 Holt-Winters RMSE: 10.45179 STL RMSE: 3.681927 ARIMA RMSE: 10.49191
RMSE for category: Drugs Naive RMSE: 8.704508 Mean RMSE: 10.54179 Holt-Winters RMSE: 7.788851 STL RMSE: 1.216346 ARIMA RMSE: 7.125262
RMSE for category: Missing Person Naive RMSE: 2.625713 Mean RMSE: 2.252828 Holt-Winters RMSE: 2.18036 STL RMSE: 0.5578251 ARIMA RMSE: 2.057782
RMSE for category: Motor Vehicle Theft Naive RMSE: 5.101007 Mean RMSE: 5.950275 Holt-Winters RMSE: 4.714105 STL RMSE: 0.9927359 ARIMA RMSE: 4.222176
RMSE for category: Weapons Naive RMSE: 2.159665 Mean RMSE: 1.764051 Holt-Winters RMSE: 1.70406 STL RMSE: 0.3049746 ARIMA RMSE: 1.577494
RMSE for category: Traffic Except DWI Naive RMSE: 4.59874 Mean RMSE: 8.062352 Holt-Winters RMSE: 4.046414 STL RMSE: 0.6869745 ARIMA RMSE: 3.797009
RMSE for category: Aggravated Assault Naive RMSE: 2.502233 Mean RMSE: 1.799438 Holt-Winters RMSE: 1.91639 STL RMSE: 0.1886339 ARIMA RMSE: 1.775804
RMSE for category: Stolen Property Naive RMSE: 1.617634 Mean RMSE: 1.141253 Holt-Winters RMSE: 1.284778 STL RMSE: 0.2934632 ARIMA RMSE: 1.138896
RMSE for category: Alcohol Offenses Naive RMSE: 1.571527 Mean RMSE: 1.22936 Holt-Winters RMSE: 1.392433 STL RMSE: 0.2721775 ARIMA RMSE: 1.183851
RMSE for category: Drunkenness Naive RMSE: 1.36626 Mean RMSE: 1.078385 Holt-Winters RMSE: 1.16832 STL RMSE: 0.2647226 ARIMA RMSE: 1.043563
RMSE for category: DUI Naive RMSE: 5.371744 Mean RMSE: 10.79571 Holt-Winters RMSE: 4.745643 STL RMSE: 0.9076895 ARIMA RMSE: 4.577422
RMSE for category: Suicide Naive RMSE: 2.883804 Mean RMSE: 2.147559 Holt-Winters RMSE: 2.208467 STL RMSE: 0.3338795 ARIMA RMSE: 2.095057
RMSE for category: Arson Naive RMSE: 1.101086 Mean RMSE: 0.7863486 Holt-Winters RMSE: 0.8619329 STL RMSE: 0.2284818 ARIMA RMSE: 0.7863486
RMSE for category: Embezzlement Naive RMSE: 2.580039 Mean RMSE: 2.053076 Holt-Winters RMSE: 1.989035 STL RMSE: 0.4795919 ARIMA RMSE: 1.806899
RMSE for category: Disorderly Conduct Naive RMSE: 1.472461 Mean RMSE: 1.130143 Holt-Winters RMSE: 1.235971 STL RMSE: 0.1677278 ARIMA RMSE: 1.109612
RMSE for category: Pornography Naive RMSE: 0.8009428 Mean RMSE: 0.5227998 Holt-Winters RMSE: 0.6276156 STL RMSE: 0.3017362 ARIMA RMSE: 0.5227998
RMSE for category: Calls for Service Naive RMSE: 0.3922323 Mean RMSE: 0.2618914 Holt-Winters RMSE: 0.2588865 STL RMSE: 0.1847502 ARIMA RMSE: 0.2618914
RMSE for category: Non Criminal Detain Naive RMSE: 4.862824 Mean RMSE: 5.339571 Holt-Winters RMSE: 4.50186 STL RMSE: 2.273436 ARIMA RMSE: 3.577469 Overall, the forecast suggests a slight decline in crime rates in the near future, followed by minor fluctuations. The trend indicates that crime levels are likely to stabilize and remain close to the current levels by the end of the year. r The RMSE values from different forecasting methods highlight their predictive accuracy for the given time series data. Among the methods, the Moving Average with a window size of 3 (MA3) achieves the lowest RMSE (28.70), suggesting it provides the most accurate forecasts. The Holt-Winters (HW) method also performs well (RMSE: 42.97), capturing trends and seasonality effectively. In contrast, the Naive method has the highest RMSE (55.76), indicating less reliable predictions. These results emphasize the importance of selecting the most suitable method, like MA3, for forecasting in this context. Based on the individual forecasts for various crime categories, the analysis reveals distinct trends. Larceny, forgery, drugs, missing person, motor vehicle theft, and stolen property initially show a decrease, with stolen property subsequently increasing. Vandalism, burglary, fraud, weapons offenses, and suicide are projected to rise, albeit at varying rates. Simple assault, alcohol-related offenses, DUI, aggravated assault, arson, embezzlement, and other offenses are expected to remain stable, with minor fluctuations in some cases. Traffic violations, excluding DWI, are predicted to either decline slightly or remain steady. These insights provide a nuanced understanding of potential future trends in crime rates across different categories. The RMSE values highlight the accuracy of different forecasting methods, with lower values indicating better performance. STL decomposition consistently achieves the lowest RMSE across most categories, making it the most reliable method, particularly for crimes like Larceny, Vandalism, and Forgery. ARIMA and Holt-Winters also perform well in capturing trends and seasonality, while Naive and Mean forecasts generally have higher RMSE, indicating lower accuracy. These comparisons guide the selection of effective models for forecasting crime trends.
Call: lm(formula = Lon ~ Lat, data = df)
Residuals: Min 1Q Median 3Q Max -0.274323 -0.029408 0.008839 0.032409 0.135637
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) -56.089368 0.124733 -449.7 <2e-16 Lat
-0.634565 0.003486 -182.0 <2e-16 — Signif. codes: 0
‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ’ ’ 1
Residual standard error: 0.03845 on 115090 degrees of freedom (6024 observations deleted due to missingness) Multiple R-squared: 0.2235, Adjusted R-squared: 0.2235 F-statistic: 3.313e+04 on 1 and 115090 DF, p-value: < 2.2e-16
The regression model shows a significant relationship between latitude and longitude, with an R-squared of 22.35%, indicating that 22.35% of longitude variance is explained by latitude. The coefficients are highly significant (p < 2.2e-16), and the residual standard error is low (0.03845), suggesting a strong but not comprehensive fit.
## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 6024 rows containing non-finite outside the scale range
## (`stat_smooth()`).## Warning: Removed 6024 rows containing missing values or values outside the scale range
## (`geom_point()`).
Here is performing simple regression on lattitude and longitude, since
the dataset has a lot of categoriacal data, regression might not be a
best strategy, however the linear regression model predicts the
longitude (Lon) based on the latitude (Lat) of crime incidents. The
scatter plot visualizes the relationship between Lat and Lon, with the
regression line (in red) showing the best fit. The summary of the
regression model includes coefficients, their significance, and overall
model metrics, providing insights into the spatial distribution of
crimes.